This module introduces widely-used mathematical methods for vectors and functions of two or more variables. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage. Tutorials and Maple worksheets will be used to support taught material.
Vectors: Cartesian coordinates; vector algebra; scalar, vector and triple products (and geometric interpretation); straight lines and planes expressed as vector equations; parametrized curves; differentiation of vector-valued functions of a scalar variable; tangent vectors; vector fields (with everyday examples)
Partial differentiation: Functions of two variables; partial differentiation (including the chain rule and change of variables); maxima, minima and saddle points; Lagrange multipliers
Integration in two dimensions: Double integrals in Cartesian coordinates; plane polar coordinates; change of variables for double integrals; line integrals; Green's theorem (statement – justification on rectangular domains only).
Total contact hours: 54
Private study hours: 96
Total study hours: 150
Method of assessment
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 hours 60%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.
E. Kreyszig, Advanced Engineering Mathematics (10th edition), John Wiley, 2011
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge of the underlying concepts and principles associated with basic mathematical methods for functions of multiple variables;
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level
of skill in calculation and manipulation of the material: vectors, partial differentiation, stationary points of functions, double integration;
3 apply the underlying concepts and principles associated with basic multiple-variable techniques in several well-defined contexts, showing an ability to evaluate the
appropriateness of different approaches to solving problems in this area;
4 make appropriate use of Maple.
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